Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2280,2,Mod(1,2280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2280.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(18.2058916609\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.23607 | 1.97905 | 0.989524 | − | 0.144370i | \(-0.0461154\pi\) | ||||
0.989524 | + | 0.144370i | \(0.0461154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | −0.372689 | −0.186344 | − | 0.982485i | \(-0.559664\pi\) | ||||
−0.186344 | + | 0.982485i | \(0.559664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.763932 | 0.211877 | 0.105938 | − | 0.994373i | \(-0.466215\pi\) | ||||
0.105938 | + | 0.994373i | \(0.466215\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.23607 | 1.14260 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.763932 | 0.141859 | 0.0709293 | − | 0.997481i | \(-0.477404\pi\) | ||||
0.0709293 | + | 0.997481i | \(0.477404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.94427 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23607 | −0.215172 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.23607 | −0.885057 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.23607 | 0.532006 | 0.266003 | − | 0.963972i | \(-0.414297\pi\) | ||||
0.266003 | + | 0.963972i | \(0.414297\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.763932 | 0.122327 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.70820 | −1.51617 | −0.758083 | − | 0.652158i | \(-0.773864\pi\) | ||||
−0.758083 | + | 0.652158i | \(0.773864\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.23607 | 0.798493 | 0.399246 | − | 0.916844i | \(-0.369272\pi\) | ||||
0.399246 | + | 0.916844i | \(0.369272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.4164 | 2.91663 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.47214 | 0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23607 | 0.166671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4721 | −1.36336 | −0.681678 | − | 0.731652i | \(-0.738749\pi\) | ||||
−0.681678 | + | 0.731652i | \(0.738749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47214 | 0.572598 | 0.286299 | − | 0.958140i | \(-0.407575\pi\) | ||||
0.286299 | + | 0.958140i | \(0.407575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.23607 | 0.659683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.763932 | −0.0947541 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52786 | 0.186658 | 0.0933292 | − | 0.995635i | \(-0.470249\pi\) | ||||
0.0933292 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4721 | 1.45975 | 0.729877 | − | 0.683579i | \(-0.239578\pi\) | ||||
0.729877 | + | 0.683579i | \(0.239578\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.47214 | −0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.763932 | 0.0819021 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.70820 | −0.181069 | −0.0905346 | − | 0.995893i | \(-0.528858\pi\) | ||||
−0.0905346 | + | 0.995893i | \(0.528858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.94427 | −0.927478 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.76393 | −0.483704 | −0.241852 | − | 0.970313i | \(-0.577755\pi\) | ||||
−0.241852 | + | 0.970313i | \(0.577755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.23607 | −0.124230 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4164 | −1.33498 | −0.667491 | − | 0.744618i | \(-0.732632\pi\) | ||||
−0.667491 | + | 0.744618i | \(0.732632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.52786 | 0.938808 | 0.469404 | − | 0.882983i | \(-0.344469\pi\) | ||||
0.469404 | + | 0.882983i | \(0.344469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.23607 | −0.510988 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.94427 | −0.864675 | −0.432338 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432338 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.47214 | −0.428353 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.23607 | 0.307154 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.47214 | −0.230528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.763932 | 0.0706255 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.4164 | 2.14658 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.70820 | −0.875359 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.23607 | 0.461010 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1803 | 1.23894 | 0.619471 | − | 0.785020i | \(-0.287347\pi\) | ||||
0.619471 | + | 0.785020i | \(0.287347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.23607 | 0.454025 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.8885 | 1.35745 | 0.678725 | − | 0.734393i | \(-0.262533\pi\) | ||||
0.678725 | + | 0.734393i | \(0.262533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.4721 | −1.22751 | −0.613755 | − | 0.789496i | \(-0.710342\pi\) | ||||
−0.613755 | + | 0.789496i | \(0.710342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.47214 | 0.208191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.944272 | −0.0789640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.763932 | −0.0634411 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.4164 | 1.68392 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.4164 | 1.42681 | 0.713404 | − | 0.700753i | \(-0.247153\pi\) | ||||
0.713404 | + | 0.700753i | \(0.247153\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.47214 | 0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.94427 | 0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4164 | −1.70922 | −0.854608 | − | 0.519274i | \(-0.826202\pi\) | ||||
−0.854608 | + | 0.519274i | \(0.826202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.472136 | −0.0374428 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9443 | 1.02015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.6525 | 1.61763 | 0.808813 | − | 0.588065i | \(-0.200110\pi\) | ||||
0.808813 | + | 0.588065i | \(0.200110\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.23607 | 0.0962278 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8885 | 1.07473 | 0.537364 | − | 0.843350i | \(-0.319420\pi\) | ||||
0.537364 | + | 0.843350i | \(0.319420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4164 | −0.955108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.0000 | −1.67263 | −0.836315 | − | 0.548250i | \(-0.815294\pi\) | ||||
−0.836315 | + | 0.548250i | \(0.815294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.23607 | 0.395810 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.4721 | −0.787134 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.4164 | −1.15228 | −0.576138 | − | 0.817352i | \(-0.695441\pi\) | ||||
−0.576138 | + | 0.817352i | \(0.695441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.47214 | 0.629729 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.47214 | 0.330590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.23607 | −0.237920 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.52786 | −0.404237 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.23607 | 0.380868 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.18034 | −0.447194 | −0.223597 | − | 0.974682i | \(-0.571780\pi\) | ||||
−0.223597 | + | 0.974682i | \(0.571780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.70820 | 0.410886 | 0.205443 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205443 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.763932 | −0.0547063 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4721 | −0.888603 | −0.444301 | − | 0.895877i | \(-0.646548\pi\) | ||||
−0.444301 | + | 0.895877i | \(0.646548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4721 | 1.30945 | 0.654727 | − | 0.755865i | \(-0.272783\pi\) | ||||
0.654727 | + | 0.755865i | \(0.272783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52786 | 0.107767 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.70820 | 0.678050 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.47214 | 0.171825 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.23607 | −0.0855006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.23607 | −0.357097 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −46.8328 | −3.17922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.4721 | 0.842789 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.41641 | 0.229812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4721 | 1.50485 | 0.752423 | − | 0.658680i | \(-0.228885\pi\) | ||||
0.752423 | + | 0.658680i | \(0.228885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.4164 | −1.41524 | −0.707618 | − | 0.706595i | \(-0.750230\pi\) | ||||
−0.707618 | + | 0.706595i | \(0.750230\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.47214 | −0.425835 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.8885 | 1.56499 | 0.782495 | − | 0.622657i | \(-0.213947\pi\) | ||||
0.782495 | + | 0.622657i | \(0.213947\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.47214 | −0.161264 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.7082 | −0.757341 | −0.378670 | − | 0.925532i | \(-0.623619\pi\) | ||||
−0.378670 | + | 0.925532i | \(0.623619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.94427 | 0.447320 | 0.223660 | − | 0.974667i | \(-0.428199\pi\) | ||||
0.223660 | + | 0.974667i | \(0.428199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.4164 | −1.30436 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.763932 | 0.0486078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.70820 | 0.234060 | 0.117030 | − | 0.993128i | \(-0.462663\pi\) | ||||
0.117030 | + | 0.993128i | \(0.462663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.05573 | −0.192112 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.47214 | −0.280056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.9443 | −1.43122 | −0.715612 | − | 0.698498i | \(-0.753852\pi\) | ||||
−0.715612 | + | 0.698498i | \(0.753852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.9443 | 1.05287 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.763932 | 0.0472862 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.05573 | 0.188424 | 0.0942121 | − | 0.995552i | \(-0.469967\pi\) | ||||
0.0942121 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.472136 | 0.0290031 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.70820 | −0.104540 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.70820 | 0.348035 | 0.174018 | − | 0.984743i | \(-0.444325\pi\) | ||||
0.174018 | + | 0.984743i | \(0.444325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.47214 | −0.150172 | −0.0750858 | − | 0.997177i | \(-0.523923\pi\) | ||||
−0.0750858 | + | 0.997177i | \(0.523923\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.23607 | −0.0745377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.4721 | −0.989715 | −0.494857 | − | 0.868974i | \(-0.664780\pi\) | ||||
−0.494857 | + | 0.868974i | \(0.664780\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.94427 | −0.535480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.2361 | −0.908908 | −0.454454 | − | 0.890770i | \(-0.650166\pi\) | ||||
−0.454454 | + | 0.890770i | \(0.650166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0689 | −1.66852 | −0.834261 | − | 0.551370i | \(-0.814105\pi\) | ||||
−0.834261 | + | 0.551370i | \(0.814105\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −50.8328 | −3.00057 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.76393 | −0.279267 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.88854 | 0.227171 | 0.113586 | − | 0.993528i | \(-0.463766\pi\) | ||||
0.113586 | + | 0.993528i | \(0.463766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4721 | 0.609711 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.23607 | −0.0717239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.88854 | 0.109217 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.4164 | 1.58026 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.4164 | −0.770752 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.47214 | −0.256074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5279 | −1.00037 | −0.500184 | − | 0.865919i | \(-0.666734\pi\) | ||||
−0.500184 | + | 0.865919i | \(0.666734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.52786 | 0.542021 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.7082 | 1.11755 | 0.558775 | − | 0.829319i | \(-0.311272\pi\) | ||||
0.558775 | + | 0.829319i | \(0.311272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8885 | −1.35026 | −0.675130 | − | 0.737699i | \(-0.735913\pi\) | ||||
−0.675130 | + | 0.737699i | \(0.735913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.23607 | −0.295019 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4721 | 0.700505 | 0.350252 | − | 0.936655i | \(-0.386096\pi\) | ||||
0.350252 | + | 0.936655i | \(0.386096\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.944272 | −0.0528691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.94427 | −0.499221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.47214 | 0.248836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.763932 | 0.0423753 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.47214 | −0.247310 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.9443 | 0.713641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.23607 | 0.177335 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.52786 | −0.0834761 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.7639 | −1.56687 | −0.783436 | − | 0.621473i | \(-0.786535\pi\) | ||||
−0.783436 | + | 0.621473i | \(0.786535\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.0557 | 0.598701 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 70.2492 | 3.79310 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.47214 | −0.133095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.0000 | −1.07366 | −0.536828 | − | 0.843692i | \(-0.680378\pi\) | ||||
−0.536828 | + | 0.843692i | \(0.680378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.9443 | 0.585833 | 0.292917 | − | 0.956138i | \(-0.405374\pi\) | ||||
0.292917 | + | 0.956138i | \(0.405374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.763932 | 0.0407757 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.9443 | −0.795403 | −0.397702 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397702 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.4164 | 1.23933 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.1803 | −1.17063 | −0.585317 | − | 0.810805i | \(-0.699030\pi\) | ||||
−0.585317 | + | 0.810805i | \(0.699030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.47214 | −0.497158 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4721 | −0.652821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.2361 | −1.52611 | −0.763055 | − | 0.646333i | \(-0.776302\pi\) | ||||
−0.763055 | + | 0.646333i | \(0.776302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.70820 | −0.505389 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.47214 | −0.128347 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.23607 | −0.374669 | −0.187335 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187335 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.583592 | 0.0300565 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.88854 | 0.0970080 | 0.0485040 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485040 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.0000 | 1.02463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.88854 | −0.505281 | −0.252640 | − | 0.967560i | \(-0.581299\pi\) | ||||
−0.252640 | + | 0.967560i | \(0.581299\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.47214 | 0.329851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.23607 | 0.266164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.8328 | 1.66469 | 0.832345 | − | 0.554258i | \(-0.186998\pi\) | ||||
0.832345 | + | 0.554258i | \(0.186998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0557 | 0.559112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1803 | 0.715304 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.58359 | −0.330421 | −0.165211 | − | 0.986258i | \(-0.552830\pi\) | ||||
−0.165211 | + | 0.986258i | \(0.552830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.23607 | 0.262131 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.2361 | −1.16035 | −0.580177 | − | 0.814490i | \(-0.697017\pi\) | ||||
−0.580177 | + | 0.814490i | \(0.697017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.83282 | −0.340367 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.47214 | 0.221133 | 0.110566 | − | 0.993869i | \(-0.464734\pi\) | ||||
0.110566 | + | 0.993869i | \(0.464734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.8885 | 0.783724 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −54.8328 | −2.69815 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.4721 | −0.708704 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.1803 | −1.08358 | −0.541790 | − | 0.840514i | \(-0.682253\pi\) | ||||
−0.541790 | + | 0.840514i | \(0.682253\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.8328 | −1.21028 | −0.605139 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605139 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.47214 | 0.120199 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.47214 | 0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.4164 | 1.13320 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.944272 | −0.0455899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.3050 | 1.21890 | 0.609448 | − | 0.792826i | \(-0.291391\pi\) | ||||
0.609448 | + | 0.792826i | \(0.291391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.763932 | 0.0367122 | 0.0183561 | − | 0.999832i | \(-0.494157\pi\) | ||||
0.0183561 | + | 0.999832i | \(0.494157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.763932 | −0.0366277 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.47214 | 0.118258 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4164 | 0.972210 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.4164 | 0.922501 | 0.461251 | − | 0.887270i | \(-0.347401\pi\) | ||||
0.461251 | + | 0.887270i | \(0.347401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.70820 | 0.0809766 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.4164 | 0.823768 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.70820 | −0.458158 | −0.229079 | − | 0.973408i | \(-0.573571\pi\) | ||||
−0.229079 | + | 0.973408i | \(0.573571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.8328 | 0.787406 | 0.393703 | − | 0.919238i | \(-0.371194\pi\) | ||||
0.393703 | + | 0.919238i | \(0.371194\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.47214 | 0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.47214 | −0.394587 | −0.197293 | − | 0.980344i | \(-0.563215\pi\) | ||||
−0.197293 | + | 0.980344i | \(0.563215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.5967 | 1.18958 | 0.594791 | − | 0.803880i | \(-0.297235\pi\) | ||||
0.594791 | + | 0.803880i | \(0.297235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.94427 | 0.414781 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.58359 | −0.212103 | −0.106052 | − | 0.994361i | \(-0.533821\pi\) | ||||
−0.106052 | + | 0.994361i | \(0.533821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.4164 | −0.986816 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.47214 | −0.297589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.472136 | −0.0216176 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.1803 | −0.647916 | −0.323958 | − | 0.946071i | \(-0.605014\pi\) | ||||
−0.323958 | + | 0.946071i | \(0.605014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.47214 | 0.112720 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.9443 | 0.588985 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.76393 | 0.216319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.58359 | 0.207702 | 0.103851 | − | 0.994593i | \(-0.466883\pi\) | ||||
0.103851 | + | 0.994593i | \(0.466883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.6525 | 0.933937 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.6525 | −1.47359 | −0.736793 | − | 0.676119i | \(-0.763661\pi\) | ||||
−0.736793 | + | 0.676119i | \(0.763661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.41641 | 0.153867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.23607 | 0.0555571 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.4164 | −0.511069 | −0.255534 | − | 0.966800i | \(-0.582251\pi\) | ||||
−0.255534 | + | 0.966800i | \(0.582251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8885 | 0.620494 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9443 | −0.577157 | −0.288578 | − | 0.957456i | \(-0.593183\pi\) | ||||
−0.288578 | + | 0.957456i | \(0.593183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.4164 | 0.597022 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.4164 | −0.551432 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.2918 | 1.34266 | 0.671330 | − | 0.741158i | \(-0.265723\pi\) | ||||
0.671330 | + | 0.741158i | \(0.265723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 65.3050 | 2.88892 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.52786 | −0.419848 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.05573 | −0.134391 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.0000 | −0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2918 | −1.15186 | −0.575932 | − | 0.817497i | \(-0.695361\pi\) | ||||
−0.575932 | + | 0.817497i | \(0.695361\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.944272 | −0.0412901 | −0.0206451 | − | 0.999787i | \(-0.506572\pi\) | ||||
−0.0206451 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.23607 | 0.228521 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −40.0000 | −1.74243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.4721 | −0.454452 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.41641 | −0.321240 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.94427 | 0.386695 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.4164 | −0.665267 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.2361 | −1.08699 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7771 | −1.28022 | −0.640108 | − | 0.768285i | \(-0.721111\pi\) | ||||
−0.640108 | + | 0.768285i | \(0.721111\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.47214 | 0.363574 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.47214 | 0.191565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.3050 | −1.59504 | −0.797522 | − | 0.603289i | \(-0.793856\pi\) | ||||
−0.797522 | + | 0.603289i | \(0.793856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.47214 | 0.190866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.763932 | 0.0325446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.23607 | −0.137363 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.8328 | 1.39117 | 0.695586 | − | 0.718443i | \(-0.255145\pi\) | ||||
0.695586 | + | 0.718443i | \(0.255145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.52786 | −0.233387 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.88854 | −0.416752 | −0.208376 | − | 0.978049i | \(-0.566818\pi\) | ||||
−0.208376 | + | 0.978049i | \(0.566818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.23607 | 0.219894 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.5410 | −1.36419 | −0.682095 | − | 0.731263i | \(-0.738931\pi\) | ||||
−0.682095 | + | 0.731263i | \(0.738931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.3050 | −0.891584 | −0.445792 | − | 0.895136i | \(-0.647078\pi\) | ||||
−0.445792 | + | 0.895136i | \(0.647078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.18034 | −0.258187 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.47214 | 0.103095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.05573 | −0.376995 | −0.188497 | − | 0.982074i | \(-0.560362\pi\) | ||||
−0.188497 | + | 0.982074i | \(0.560362\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.70820 | 0.237225 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.9443 | 0.868915 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.583592 | 0.0241699 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.763932 | −0.0315847 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.4164 | −0.471206 | −0.235603 | − | 0.971849i | \(-0.575706\pi\) | ||||
−0.235603 | + | 0.971849i | \(0.575706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.94427 | −0.368542 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4721 | −0.513035 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.4164 | −0.959979 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.4721 | 0.756014 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 47.4164 | 1.93738 | 0.968691 | − | 0.248270i | \(-0.0798619\pi\) | ||||
0.968691 | + | 0.248270i | \(0.0798619\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3607 | −0.422621 | −0.211310 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211310 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.52786 | 0.0622194 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.47214 | 0.385097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.5279 | −1.36085 | −0.680427 | − | 0.732816i | \(-0.738206\pi\) | ||||
−0.680427 | + | 0.732816i | \(0.738206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.88854 | 0.0764023 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.5279 | −1.43496 | −0.717478 | − | 0.696581i | \(-0.754704\pi\) | ||||
−0.717478 | + | 0.696581i | \(0.754704\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.70820 | 0.391473 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.3050 | −1.58236 | −0.791179 | − | 0.611585i | \(-0.790532\pi\) | ||||
−0.791179 | + | 0.611585i | \(0.790532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.3607 | 1.30069 | 0.650343 | − | 0.759641i | \(-0.274625\pi\) | ||||
0.650343 | + | 0.759641i | \(0.274625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.47214 | 0.0992034 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.94427 | −0.358345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.23607 | −0.0493638 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.4721 | 0.577042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.0000 | −0.793676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5967 | 0.617966 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.7639 | −1.76807 | −0.884035 | − | 0.467422i | \(-0.845183\pi\) | ||||
−0.884035 | + | 0.467422i | \(0.845183\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.5967 | 0.693948 | 0.346974 | − | 0.937875i | \(-0.387209\pi\) | ||||
0.346974 | + | 0.937875i | \(0.387209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.23607 | −0.206170 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.8328 | 0.583138 | 0.291569 | − | 0.956550i | \(-0.405823\pi\) | ||||
0.291569 | + | 0.956550i | \(0.405823\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.9443 | 0.508107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −46.8328 | −1.83552 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.5279 | −1.23378 | −0.616890 | − | 0.787049i | \(-0.711608\pi\) | ||||
−0.616890 | + | 0.787049i | \(0.711608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.1803 | −0.554072 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.4721 | 0.486584 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.8328 | 1.20108 | 0.600538 | − | 0.799596i | \(-0.294953\pi\) | ||||
0.600538 | + | 0.799596i | \(0.294953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3050 | 0.906458 | 0.453229 | − | 0.891394i | \(-0.350272\pi\) | ||||
0.453229 | + | 0.891394i | \(0.350272\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.41641 | 0.132682 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.23607 | −0.203046 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88854 | 0.0731247 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.4721 | 0.868823 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.52786 | −0.213401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.5967 | −1.06378 | −0.531888 | − | 0.846815i | \(-0.678517\pi\) | ||||
−0.531888 | + | 0.846815i | \(0.678517\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.5279 | 0.596784 | 0.298392 | − | 0.954443i | \(-0.403550\pi\) | ||||
0.298392 | + | 0.954443i | \(0.403550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.9443 | −0.957273 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7771 | 1.21592 | 0.607958 | − | 0.793969i | \(-0.291989\pi\) | ||||
0.607958 | + | 0.793969i | \(0.291989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.8885 | −0.607070 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.4164 | −0.817087 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.360680 | −0.0137408 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.5279 | −0.971126 | −0.485563 | − | 0.874202i | \(-0.661385\pi\) | ||||
−0.485563 | + | 0.874202i | \(0.661385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.47214 | −0.245856 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.4721 | 0.548959 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43.4164 | −1.64451 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.8885 | 0.903548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5836 | −0.550815 | −0.275407 | − | 0.961328i | \(-0.588813\pi\) | ||||
−0.275407 | + | 0.961328i | \(0.588813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.23607 | 0.122051 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.47214 | −0.0931060 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −70.2492 | −2.64199 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.3050 | −1.17568 | −0.587841 | − | 0.808976i | \(-0.700022\pi\) | ||||
−0.587841 | + | 0.808976i | \(0.700022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.1115 | −0.828081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.944272 | 0.0353138 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.7082 | −0.437251 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.23607 | 0.0460976 | 0.0230488 | − | 0.999734i | \(-0.492663\pi\) | ||||
0.0230488 | + | 0.999734i | \(0.492663\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.8885 | 1.85795 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.94427 | 0.258260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.763932 | 0.0283717 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6525 | 0.765958 | 0.382979 | − | 0.923757i | \(-0.374898\pi\) | ||||
0.382979 | + | 0.923757i | \(0.374898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.4164 | 0.866087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.8328 | −1.36045 | −0.680226 | − | 0.733003i | \(-0.738118\pi\) | ||||
−0.680226 | + | 0.733003i | \(0.738118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.4164 | −0.753071 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.88854 | −0.0695654 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.94427 | −0.329020 | −0.164510 | − | 0.986375i | \(-0.552604\pi\) | ||||
−0.164510 | + | 0.986375i | \(0.552604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.763932 | 0.0280637 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.9443 | −1.64885 | −0.824423 | − | 0.565975i | \(-0.808500\pi\) | ||||
−0.824423 | + | 0.565975i | \(0.808500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.4164 | −0.638088 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.8328 | −1.71123 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.94427 | 0.326381 | 0.163191 | − | 0.986595i | \(-0.447821\pi\) | ||||
0.163191 | + | 0.986595i | \(0.447821\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.70820 | 0.135134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.94427 | −0.107011 | −0.0535057 | − | 0.998568i | \(-0.517040\pi\) | ||||
−0.0535057 | + | 0.998568i | \(0.517040\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.05573 | −0.110916 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.41641 | 0.341345 | 0.170672 | − | 0.985328i | \(-0.445406\pi\) | ||||
0.170672 | + | 0.985328i | \(0.445406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.4164 | −0.847731 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.47214 | −0.161690 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.11146 | 0.292507 | 0.146253 | − | 0.989247i | \(-0.453279\pi\) | ||||
0.146253 | + | 0.989247i | \(0.453279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.9443 | −0.826318 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.5279 | 1.42172 | 0.710859 | − | 0.703334i | \(-0.248306\pi\) | ||||
0.710859 | + | 0.703334i | \(0.248306\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.94427 | −0.321288 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.9443 | 0.607872 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.70820 | −0.347833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.763932 | 0.0273007 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.4164 | 0.764384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.8328 | 0.386148 | 0.193074 | − | 0.981184i | \(-0.438154\pi\) | ||||
0.193074 | + | 0.981184i | \(0.438154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.05573 | 0.108787 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.4721 | −0.372346 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41641 | 0.121320 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.472136 | 0.0167449 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.7771 | 1.33813 | 0.669067 | − | 0.743202i | \(-0.266694\pi\) | ||||
0.669067 | + | 0.743202i | \(0.266694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0557 | 0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.70820 | −0.0603564 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.4164 | −0.544033 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.9443 | −0.456226 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.70820 | 0.200938 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.9443 | 1.36921 | 0.684604 | − | 0.728915i | \(-0.259975\pi\) | ||||
0.684604 | + | 0.728915i | \(0.259975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.944272 | 0.0331579 | 0.0165789 | − | 0.999863i | \(-0.494723\pi\) | ||||
0.0165789 | + | 0.999863i | \(0.494723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.47214 | −0.0867016 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.6525 | −0.723425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.23607 | 0.183187 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.5279 | 0.541926 | 0.270963 | − | 0.962590i | \(-0.412658\pi\) | ||||
0.270963 | + | 0.962590i | \(0.412658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.18034 | −0.0760019 | −0.0380009 | − | 0.999278i | \(-0.512099\pi\) | ||||
−0.0380009 | + | 0.999278i | \(0.512099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.23607 | −0.0430344 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.00000 | 0.278187 | 0.139094 | − | 0.990279i | \(-0.455581\pi\) | ||||
0.139094 | + | 0.990279i | \(0.455581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.3050 | 1.64297 | 0.821484 | − | 0.570231i | \(-0.193146\pi\) | ||||
0.821484 | + | 0.570231i | \(0.193146\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.4721 | −0.571412 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 91.3050 | 3.16353 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8885 | −0.480633 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.94427 | −0.309159 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4164 | −0.979876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.2361 | −0.524758 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4164 | 0.427137 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.5967 | −1.70416 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.0689 | −0.963322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.7214 | 1.46275 | 0.731376 | − | 0.681975i | \(-0.238879\pi\) | ||||
0.731376 | + | 0.681975i | \(0.238879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4721 | 0.835952 | 0.417976 | − | 0.908458i | \(-0.362740\pi\) | ||||
0.417976 | + | 0.908458i | \(0.362740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.8328 | 0.369611 | 0.184805 | − | 0.982775i | \(-0.440834\pi\) | ||||
0.184805 | + | 0.982775i | \(0.440834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −50.8328 | −1.73238 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.8328 | 1.59421 | 0.797104 | − | 0.603842i | \(-0.206364\pi\) | ||||
0.797104 | + | 0.603842i | \(0.206364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0000 | 0.748022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.00000 | 0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.16718 | 0.0395485 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.76393 | −0.161235 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.23607 | −0.177011 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.7082 | 1.27332 | 0.636658 | − | 0.771146i | \(-0.280316\pi\) | ||||
0.636658 | + | 0.771146i | \(0.280316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.88854 | 0.131157 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.3050 | −1.86327 | −0.931636 | − | 0.363394i | \(-0.881618\pi\) | ||||
−0.931636 | + | 0.363394i | \(0.881618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5967 | 0.861399 | 0.430700 | − | 0.902495i | \(-0.358267\pi\) | ||||
0.430700 | + | 0.902495i | \(0.358267\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.4721 | 0.352017 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.8885 | −0.869252 | −0.434626 | − | 0.900611i | \(-0.643119\pi\) | ||||
−0.434626 | + | 0.900611i | \(0.643119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 104.721 | 3.51224 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.23607 | −0.0414098 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.47214 | 0.0827269 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4164 | 0.515314 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.88854 | 0.0630566 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.83282 | −0.227887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.11146 | −0.0703428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.4164 | 0.912361 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.47214 | −0.281623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.1115 | 0.335745 | 0.167873 | − | 0.985809i | \(-0.446310\pi\) | ||||
0.167873 | + | 0.985809i | \(0.446310\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.4164 | −0.444994 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.7771 | −1.45040 | −0.725200 | − | 0.688538i | \(-0.758253\pi\) | ||||
−0.725200 | + | 0.688538i | \(0.758253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.94427 | −0.163632 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.47214 | −0.147844 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 74.2492 | 2.45193 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0000 | −0.791687 | −0.395843 | − | 0.918318i | \(-0.629548\pi\) | ||||
−0.395843 | + | 0.918318i | \(0.629548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.5279 | −0.577563 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.23607 | 0.106401 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.52786 | 0.312936 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.8885 | 0.914993 | 0.457497 | − | 0.889211i | \(-0.348746\pi\) | ||||
0.457497 | + | 0.889211i | \(0.348746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.4164 | 0.669121 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.7082 | 0.645218 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.52786 | 0.180780 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.4164 | −1.22234 | −0.611170 | − | 0.791499i | \(-0.709301\pi\) | ||||
−0.611170 | + | 0.791499i | \(0.709301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8885 | −0.779573 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.1246 | −0.558246 | −0.279123 | − | 0.960255i | \(-0.590044\pi\) | ||||
−0.279123 | + | 0.960255i | \(0.590044\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | −0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.23607 | −0.170329 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.52786 | 0.309288 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.4721 | 0.404437 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.9443 | 1.39110 | 0.695551 | − | 0.718477i | \(-0.255160\pi\) | ||||
0.695551 | + | 0.718477i | \(0.255160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.18034 | 0.199991 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.944272 | −0.0305240 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 83.1935 | 2.68646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.0000 | 1.58065 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.94427 | −0.288225 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.70820 | −0.183754 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1803 | −0.584640 | −0.292320 | − | 0.956321i | \(-0.594427\pi\) | ||||
−0.292320 | + | 0.956321i | \(0.594427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.47214 | 0.143666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.8328 | −1.24620 | −0.623102 | − | 0.782140i | \(-0.714128\pi\) | ||||
−0.623102 | + | 0.782140i | \(0.714128\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −75.7771 | −2.42930 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.763932 | 0.0244654 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.5836 | 0.978456 | 0.489228 | − | 0.872156i | \(-0.337279\pi\) | ||||
0.489228 | + | 0.872156i | \(0.337279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.11146 | 0.0674824 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.47214 | −0.142784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.00000 | 0.127580 | 0.0637901 | − | 0.997963i | \(-0.479681\pi\) | ||||
0.0637901 | + | 0.997963i | \(0.479681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4721 | 0.397395 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.9443 | 0.412021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.9443 | 0.411604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9443 | 0.919445 | 0.459723 | − | 0.888063i | \(-0.347949\pi\) | ||||
0.459723 | + | 0.888063i | \(0.347949\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.4721 | −0.585606 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.41641 | 0.0448581 | 0.0224290 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224290 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.23607 | 0.102385 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2280.2.a.p.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6840.2.a.bd.1.2 | 2 | |||
4.3 | odd | 2 | 4560.2.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.p.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4560.2.a.be.1.1 | 2 | 4.3 | odd | 2 | |||
6840.2.a.bd.1.2 | 2 | 3.2 | odd | 2 |